Helpful: Good definitions
Put answers down for examples or else it’s pointless
Enjoyed: The definitions
The vocab was helpful
Comments: Everything was “smooshed” together, hard to pick out important info b/c it ran together
All one font and color
Very,very plain – no pictures
Need videos
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TEXT
2.1
-Relation - The mapping, or pairing, of input values with output values.
-Domain - The set of input values (x).
-Range - The set of output values (y).
-Function - A relation when there is exactly one output for each input. 2.2
-Slope - The ratio of vertical change to horizontal change (rise over run).
-Slope Formula - y‚ - y„
x‚ - x„
-Parallel - Lines that do not intersect.
-Perpendicular - When lines form 90° angles.
-Steepness -
- If two lines are positive, then the largest slope (m) is steepest.
- If two lines are negative, then the largest absolute value of the slope (|m|) is the steepest.
- If two lines are parallel, then the slope and steepness is the same.
- If two lines are perpendicular, then the slopes at opposite recipricals, and the largest is the steepest. 2.3
-Slope-intercept Form - A linear equation. y = mx + b; m = slope and b = y-intercept.
-Y-intercept - The point of a line that crosses the y-axis.
-X-intercept - The point of a line that crosses the x-axis.
-Standard Form - A linear equation. Ax + By = C; A and B are both not zero. 2.4
-Point-slope form - y - y‚ = m(x - x‚); m = slope and (x‚ , y‚) = point.
-Direct Variation - when two variables show y = kx or k = y/x and k does not equal 0.
-Constant of Variation - The k value that remains the same. 2.5
-Scatter Plot - A graph used to determine whether there is a relationship between paired data.
-Positive Correlation - When x and y values increases. -Negative Correlation - When x values increase and y values decrease.
-Relatively No Correlation - When there is no linear pattern. 2.6
-Linear Inequality - When two variables can be writen as Ax + By < C, Ax + By < C, Ax + By > C, or Ax + By > C.
-Solution (of Linear Inequality) - When an ordered pair make the inequality true.
-Half Planes - The shaded area on a coordinate plain which contains the solutions. 2.7
-Piecewise Function - A function represented by a combination of equations, each corresponding to the domain.
-Step Function - A piecewise function that resembles steps. 2.8
-Absolute Value Function - A piecewise function.
-Vertex - The corner point of a function on the graph.
Practice problems!!!!!
2.1 Functions and their Graphs
Example You can represent a relation with a table of values or a graph of ordered pairs.
X
0
1
3
Y
5
3
4
Graph the relation. Then state whether it’s a function.
1.
X
-4
7
3
Y
6
-3
4
2.
X
6
5
11
Y
-4&9
3
5
2.2 Slope and Rate of Change
Example
You can find the slope of a line passing through 2 given points.
Points: (4,2) and (-3,5)
Slope: m= y2 - y1 = 5-4 = -1
x2- x1 -3-4 7
Find the slope of the line passing through the given points.
1. ( 2,4), (5,7)
2. (5,3), (0,0)
3. (1,5), (6,0)
2.3 Quick Graphs of Linear Equations
Example
You can graph a linear equation in slope-intercept form or in standard form.
Linear Standard Form
Y=-3+1 4x-3y=12
Slope= -3 x-intercept= 3
y-intercept= 1 y-intercept= -4
2.4 Writing Equations of Lines
Example
You can write an equation of a line using (1.) the slope and y-intercept,
(2.) the slope and a point on the line, or (3.) two points on the line.
1. Slope-intercept form, m=2, b=-3 y=2x-3
2. Point-slope form, m=2, (x1,y2) = (2,1) y-1=2(x-2)
y= 2x-3
3. Points (0,-3) and (2,1) slope= 1-(-3) = 2
2-0
Y=2x-3
Write and equation of the line that has the given properties.
1. Slope: -1, y-intercept: 2
2. Slope: 3, y-intercept: (-4,1)
3. Points: (3,-8), (8,2)
2.5 Correlation and Best-Fitting Lines
Example
You can graph data to see what relation, if any, exist. The table shows the price, p (in dollars per lb ) of bread where t is the number of years since 1990.
T
0
1
2
3
4
5
6
P
.70
.72
.74
.76
.78
.84
.87
Approximate the best-fitting line using (4, .80) and (6, .85), .85-.80 y=-.80=.025(x-4)
m= 6-4 =.025 y=.025 + .70
Approximate the best fitting line for the data.
1.
X
14
11
21
3
4
19
10
1
17
6
Y
4
6
1
10
9
0
5
10
2
7
2.6 Linear Inequalities in Two Variables
Example
You can graph a linear inequality in 2 variables in a coordinate plane.
To graph Y<x+2, first graph the boundary line, Y=x+2. Use a dashed line since the symbol is < , and not <. Test the point (0,0) is a solution of the inequality, shade the half-plane that contains it. (Right)
Graph the inequality in a coordinate plane.
1. 2x<6
2. Y> -x+4
3. Y < 7
2.7 Piecewise Functions
Example
You can graph a piece wise function by graphing each piece separately.
Y={ x-1, if x<0 ¬ Open circle
{ -x+2, if x>0 ¬ closed circle
Graph y= x-1 to the left of x=0
Graph y=-x+2 to the right of and including x=0
Graph the function.
1. Y= {2x, if x<-1
{2x+1, if x>-1
2. Y= {-x, if x<0
{3x, if x>0
2.8 Absolute Value Functions
Example
You can graph an absolute value function using symmetry.
The graph of y= 3 [ x +1 ] -2 has vertex (-1, -2). (to find the vertex of the equation, the b=y and x= the opposite of the number inside the parenthesis.)(slope = 3) Plot a second point such as (0,1). Use symmetry to plot a 3rd point,(-2, 1). Note that a=3>0 and [a] >1, so the graph opens up and is narrower than the graph of y= [x].
*note: [ ] = absolute value symbols.
1. Y= -[x] +1
2. Y= [x-4] +3
3. Y= 3[x+6] -2
Edited by Tanner Landis
Someone please post some stuff in this . This project needs to be done like pronto.
-Tanner
MATH STUFF HERE>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
October 26, 2008 4:36 pm.......still no entries-editor
PERIOD 2
Helpful: Good definitions
Put answers down for examples or else it’s pointless
Enjoyed: The definitions
The vocab was helpful
Comments: Everything was “smooshed” together, hard to pick out important info b/c it ran together
All one font and color
Very,very plain – no pictures
Need videos
Tanner whining
TEXT
2.1
-Relation - The mapping, or pairing, of input values with output values.
-Domain - The set of input values (x).
-Range - The set of output values (y).
-Function - A relation when there is exactly one output for each input.
2.2
-Slope - The ratio of vertical change to horizontal change (rise over run).
-Slope Formula -
y‚ - y„
x‚ - x„
-Parallel - Lines that do not intersect.
-Perpendicular - When lines form 90° angles.
-Steepness -
- If two lines are positive, then the largest slope (m) is steepest.
- If two lines are negative, then the largest absolute value of the slope (|m|) is the steepest.
- If two lines are parallel, then the slope and steepness is the same.
- If two lines are perpendicular, then the slopes at opposite recipricals, and the largest is the steepest.
2.3
-Slope-intercept Form - A linear equation. y = mx + b; m = slope and b = y-intercept.
-Y-intercept - The point of a line that crosses the y-axis.
-X-intercept - The point of a line that crosses the x-axis.
-Standard Form - A linear equation. Ax + By = C; A and B are both not zero.
2.4
-Point-slope form - y - y‚ = m(x - x‚); m = slope and (x‚ , y‚) = point.
-Direct Variation - when two variables show y = kx or k = y/x and k does not equal 0.
-Constant of Variation - The k value that remains the same.
2.5
-Scatter Plot - A graph used to determine whether there is a relationship between paired data.
-Positive Correlation - When x and y values increases.
-Negative Correlation - When x values increase and y values decrease.
-Relatively No Correlation - When there is no linear pattern.
2.6
-Linear Inequality - When two variables can be writen as Ax + By < C, Ax + By < C, Ax + By > C, or Ax + By > C.
-Solution (of Linear Inequality) - When an ordered pair make the inequality true.
-Half Planes - The shaded area on a coordinate plain which contains the solutions.
2.7
-Piecewise Function - A function represented by a combination of equations, each corresponding to the domain.
-Step Function - A piecewise function that resembles steps.
2.8
-Absolute Value Function - A piecewise function.
-Vertex - The corner point of a function on the graph.
Practice problems!!!!!
2.1 Functions and their Graphs
Example You can represent a relation with a table of values or a graph of ordered pairs.
Graph the relation. Then state whether it’s a function.
1.
2.
2.2 Slope and Rate of Change
Example
You can find the slope of a line passing through 2 given points.
Points: (4,2) and (-3,5)
Slope: m= y2 - y1 = 5-4 = -1
x2- x1 -3-4 7
Find the slope of the line passing through the given points.
1. ( 2,4), (5,7)
2. (5,3), (0,0)
3. (1,5), (6,0)
2.3 Quick Graphs of Linear Equations
Example
You can graph a linear equation in slope-intercept form or in standard form.
Linear Standard Form
Y=-3+1 4x-3y=12
Slope= -3 x-intercept= 3
y-intercept= 1 y-intercept= -4
Graph the equation
1. Y= -x+3
2. -3x+y= 5
3. 6x-y= 2
2.4 Writing Equations of Lines
Example
You can write an equation of a line using (1.) the slope and y-intercept,
(2.) the slope and a point on the line, or (3.) two points on the line.
1. Slope-intercept form, m=2, b=-3 y=2x-3
2. Point-slope form, m=2, (x1,y2) = (2,1) y-1=2(x-2)
y= 2x-3
3. Points (0,-3) and (2,1) slope= 1-(-3) = 2
2-0
Y=2x-3
Write and equation of the line that has the given properties.
1. Slope: -1, y-intercept: 2
2. Slope: 3, y-intercept: (-4,1)
3. Points: (3,-8), (8,2)
2.5 Correlation and Best-Fitting Lines
Example
You can graph data to see what relation, if any, exist. The table shows the price, p (in dollars per lb ) of bread where t is the number of years since 1990.
Approximate the best-fitting line using (4, .80) and (6, .85),
.85-.80 y=-.80=.025(x-4)
m= 6-4 =.025 y=.025 + .70
Approximate the best fitting line for the data.
1.
2.6 Linear Inequalities in Two Variables
Example
You can graph a linear inequality in 2 variables in a coordinate plane.
To graph Y<x+2, first graph the boundary line, Y=x+2. Use a dashed line since the symbol is < , and not <. Test the point (0,0) is a solution of the inequality, shade the half-plane that contains it. (Right)
Graph the inequality in a coordinate plane.
1. 2x<6
2. Y> -x+4
3. Y < 7
2.7 Piecewise Functions
Example
You can graph a piece wise function by graphing each piece separately.
Y={ x-1, if x<0 ¬ Open circle
{ -x+2, if x>0 ¬ closed circle
Graph y= x-1 to the left of x=0
Graph y=-x+2 to the right of and including x=0
Graph the function.
1. Y= {2x, if x<-1
{2x+1, if x>-1
2. Y= {-x, if x<0
{3x, if x>0
2.8 Absolute Value Functions
Example
You can graph an absolute value function using symmetry.
The graph of y= 3 [ x +1 ] -2 has vertex (-1, -2). (to find the vertex of the equation, the b=y and x= the opposite of the number inside the parenthesis.)(slope = 3) Plot a second point such as (0,1). Use symmetry to plot a 3rd point,(-2, 1). Note that a=3>0 and [a] >1, so the graph opens up and is narrower than the graph of y= [x].
*note: [ ] = absolute value symbols.
1. Y= -[x] +1
2. Y= [x-4] +3
3. Y= 3[x+6] -2
Edited by Tanner Landis
Someone please post some stuff in this . This project needs to be done like pronto.
-Tanner
MATH STUFF HERE>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
October 26, 2008 4:36 pm.......still no
entries -editor